The invention is in the field of well logging, in which measurements taken in boreholes are used in searching for and exploiting valuable underground resources such as oil and gas, and concerns improving logs to account for the effect on a log measurement both of the bed in which it is taken and of one or more other beds.
A measurement taken with a logging tool at a given depth level in a borehole typically is influenced by the formation at that depth level as well as by the formation at other depth levels, which may well be in other subsurface beds, and by the inherent characteristics of the tool itself. It has been proposed to use a linear filter to approximate the tool response and thereby seek to remove it, particularly in the case of the induction log response at low conductivities. See Doll, H. G., Introduction to Induction Logging and Application to Logging of Wells Drilled With Oil-Base Mud, J.P.T., Vol. 1, No. 6, June 1949. It is believed that while this technique gives good results at low formation conductivities, it is not sufficiently accurate at medium and high conductivities, probably due to skin effect and associated nonlinearities of the tool response. It has been proposed, in addition, to adapt the linear filter proposal in order to account for skin effect, by providing different linear filters for different conductivities, and filter charts have been developed for the purpose. Still in addition, it has been proposed to use a layered model and a linear filter for each conductivity assuming infinitely homogeneous formations. See U.K. patent specification No. 1405311 and U.S. patent applications Ser. Nos. 019,917 (now U.S. Pat. No. 4,314,338); 019,918 (now U.S. Pat. No. 4,340,934); 019,925 (now U.S. Pat. No. 4,314,339) and 019,926 (now U.S. Pat. No. 4,313,164) filed on Mar. 12, 1979 and assigned to the assignee of this application. While it is believed that these techniques are suitable in many conductivity situations, it is also believed that they may not be highly accurate in others--e.g., in high conductivity situations or when there is a significant conductivity contrast across a bed boundary. One difficulty particularly relevant to the latter case is that there is no obvious way to combine two different linear filters, one for each conductivity on either side of a boundary, in such a way as to correctly reconstruct the induction response across that boundary. The effect of many boundaries is yet more complicated and potentially more troublesome. One simplified example of nonlinearities in induction logs can be visualized by considering the basic magnetic field which would be established by the transmitting coils of a tool had they been in a vacuum and the degrading of this basic field by the out-of-phase coupling field generated by eddy currents circulating in the formation. It can be observed intuitively that a linear filter could account sufficiently accurately for the coupling field within an infinitely homogeneous medium but not for coupling effects which reach across a bed boundary.
The invention herein provides a process which remains linear and yet can account for nonlinear couplings across bed boundaries, and can do this efficiently enough to make its use practical in improving actual logs derived in boreholes having the typical nonlinearities associated therewith. More specifically, the invented process makes use of the discovery that a log can be considered as being made of basic building blocks which can be superposed linearly, and that each such basic building block is the log response across a given step from one semi-infinite homogeneous bed to another. In the example of an induction log, one aspect of the discovery is that the tool response when moved across a boundary between a first bed having a first conductivity and a second bed having a second conductivity can be derived by superposing (i) the tool responses when the tool is moved from a hypothetical semi-infinite bed having near zero conductivity to a hypothetical semi-infinite layer having the conductivity of the first layer and (ii) the tool response when moved from the hypothetical semi-infinite layer having near zero conductivity to the second layer. An additional aspect, for the same example, is that the conductivity log in a second layer which is a thin bed sandwiched between a first and a third layer can be reconstructed by linearly superposing the responses at the transitions between (i) the first and second layers and (ii) the second and third layers, and removing from the result of this superposition the conductivity of the second layer.
In particular embodiments of the invention, an original log is converted into an improved log which accounts for the coupling across one or more bed boundaries in a process involving the following overall steps: finding, for example from the original induction log, a provisional layered formation characterized by the depth levels of provisional bed boundaries and provisional characteristics of the respective beds or layers (e.g., the provisional conductivity or resistivity of a layer); deriving a provisional reconstructed log from the provisional layered formation characteristics by superposing step profiles determined by the boundaries and the layer characteristics of the provisional layered formations; matching the original log against the provisional reconstructed log; refining the provisional layered formation on the basis of this; repeating such matching and refining until the original log and the most recently improved provisionally reconstructed log match within selected limits; and converting the original log to a corrected, and thereby improved, log on the basis of the finalized layered formation characteristics and/or producing a rectangularized induction log based on said finalized layered formation characteristics.
An improved induction log produced in accordance with the invention tends to have sharper vertical response and tends to have the logged parameter restored closer to its true level at least in thinner beds as compared with the original log. For example, the vertical resolution of induction logs tends to be improved to approximate that of other logs, such as those tradenamed Laterologs by the assignee of this application, so that better depth alignment can be made between the improved induction logs and other logs which have an inherently higher initial resolution. As another nonlimiting example, induction logs improved in accordance with the invention avoid difficulties ensuing when inaccurate induction logs are used to find hydrocarbon saturation on the basis of which reserves are estimated--possibly with large errors especially for thin hydrocarbon beds. In the case of a Laterolog, which starts out with adequate vertical resolution and is improved in accordance with a modification of the above process, the improvement is mainly in the response to beds which are next to, or squeezed between, other beds of greatly different resistivity. Yet another modification of the above process relates to improving an induction log by building the initial provisional layered formation characteristic on the basis of a Laterolog of the same subsurface formations.